Middle School Math Quiz
5 posters
Page 1 of 1
Middle School Math Quiz
Again questions from a math magazine.
1. Three pennies showing 2 heads and 1 tail lie on a table. Two of the coins are selected at random and turned over. What is the probability that now all three coins show the same side?
2. Anna and Bob play a game in which Anna begins by rolling a fair die, after which Bob tosses a fair coin. They take turns until one of them wins. Anna wins when she rolls a 6; Bob wins when the coin lands heads. What is the probability that Anna wins the game?
3. What is the average of all multiples of 7 between 7 and 777, inclusive? Please show two different ways of solving this problem, by using a simple formula, and by using simple commonsense.
4. The odometer of a family car shows 15,951 miles. The driver noticed that this number is palindromic (read the same forward or backward). Surprised, the driver saw his 3rd palindromic odometer reading (not counting 15,951) exactly 5 hours later. What is the car’s speed in mph over those 5 hours?
5. The fifth term of a geometric series is 5! And the sixth term is 6!. What is the fourth term?
1. Three pennies showing 2 heads and 1 tail lie on a table. Two of the coins are selected at random and turned over. What is the probability that now all three coins show the same side?
2. Anna and Bob play a game in which Anna begins by rolling a fair die, after which Bob tosses a fair coin. They take turns until one of them wins. Anna wins when she rolls a 6; Bob wins when the coin lands heads. What is the probability that Anna wins the game?
3. What is the average of all multiples of 7 between 7 and 777, inclusive? Please show two different ways of solving this problem, by using a simple formula, and by using simple commonsense.
4. The odometer of a family car shows 15,951 miles. The driver noticed that this number is palindromic (read the same forward or backward). Surprised, the driver saw his 3rd palindromic odometer reading (not counting 15,951) exactly 5 hours later. What is the car’s speed in mph over those 5 hours?
5. The fifth term of a geometric series is 5! And the sixth term is 6!. What is the fourth term?
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
1. 1/3
2. 1/12
3. (7+7*2+7*3..+7*111)/111 = (7*(1+2+3+...111))/111 = 7*112/2 = 392
common sense
(7+777)/2 = 392
4. 1st is 16061, 2nd palindromic # is 16161, 3rd one is 16261  so 1626115951/5 = 62mph
5. 20
2. 1/12
3. (7+7*2+7*3..+7*111)/111 = (7*(1+2+3+...111))/111 = 7*112/2 = 392
common sense
(7+777)/2 = 392
4. 1st is 16061, 2nd palindromic # is 16161, 3rd one is 16261  so 1626115951/5 = 62mph
5. 20
Hellsangel Posts : 14721
Join date : 20110428
Re: Middle School Math Quiz
Hellsangel wrote:
The answer posted for #2, 1/12 is incorrect.
Others are fine.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
For 2... in any round, Bob has 1 in 2 odds of winning while Anna only 1 in 6. So Bob is thrice as likely to win as Anna. One of them must win or the game won't stop. So Anna's probability is 1/4.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
What about a 'draw'?charvaka wrote:For 2... in any round, Bob has 1 in 2 odds of winning while Anna only 1 in 6. So Bob is thrice as likely to win as Anna. One of them must win or the game won't stop. So Anna's probability is 1/4.
Hellsangel Posts : 14721
Join date : 20110428
Re: Middle School Math Quiz
I assumed, if it's a draw, they play another round.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
charvaka wrote:For 2... in any round, Bob has 1 in 2 odds of winning while Anna only 1 in 6. So Bob is thrice as likely to win as Anna. One of them must win or the game won't stop. So Anna's probability is 1/4.
Sorry, incorrect answer.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
indophile wrote:Again questions from a math magazine.
1. Three pennies showing 2 heads and 1 tail lie on a table. Two of the coins are selected at random and turned over. What is the probability that now all three coins show the same side?
1/3
Re: Middle School Math Quiz
To harharmahadev  Your answer, 1/3 for # 1 ia correct.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
There are 12 outcomescharvaka wrote:I assumed, if it's a draw, they play another round.
1  H
1  T
2  H
2  T
3  H
3  T
4  H
4  T
5  H
5  T
6  H
6  T
of these only 6  T is the winning option for Anna
So isn't it 1/12?
Hellsangel Posts : 14721
Join date : 20110428
Re: Middle School Math Quiz
charvaka wrote:I assumed, if it's a draw, they play another round.
Right, like the question says  "they take turns until someone wins."
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
indophile wrote:Again questions from a math magazine.
2. Anna and Bob play a game in which Anna begins by rolling a fair die, after which Bob tosses a fair coin. They take turns until one of them wins. Anna wins when she rolls a 6; Bob wins when the coin lands heads. What is the probability that Anna wins the game?
If Anna and Bob were playing some stripapieceofclothing off with this game, then Anna is going to be buck naked well before Bob....even considering the fact that females have a lot more clothes than men.
Re: Middle School Math Quiz
That's if they play only one round... if Anna doesn't win round 1 and Bob doesn't win it either (6H), then they play round 2.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
Probabilty of her winning 2/7?
1/6+5/6*1/2*1/6+5/6*1/2*5/6*1/2*1/6+till infinity
1/6+5/6*1/2*1/6+5/6*1/2*5/6*1/2*1/6+till infinity
Mosquito Posts : 706
Join date : 20110428
Re: Middle School Math Quiz
PseudoIntellectual wrote:Probabilty of her winning 2/7?
1/6+5/6*1/2*1/6+5/6*1/2*5/6*1/2*1/6+till infinity
Perfect!
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
Question # 2. PI got it.
The answer is 2/7. The probability that Anna wins is the probability that she wins on her first turn or her second turn or her third turn, and so on. The probability distribution, in which we observe a string of failures before the first success is called the geometric probability distribution. The probability that Anna wins on the first roll is 1/6. For Anna to win on the second roll, she must roll any number except 6 on her first roll and Bob must toss tails on his first toss. The probability that Anna wins on the second roll is (5/6)(1/2)(1/6). For Anna to win on the third roll, she and Bob must each have two failures before Anna’s success: (5/6 * ½)^2 * 1/6. So we need to find the sum of infinite geometric series:
P(Anna wins) = 1/6 + (5/6 * ½) * 1/6 + (5/6 * ½)^2 * 1/6 + (5/6 * ½)^3 * 1/6 + 
We use the formula for the sum of an infinite geometric series, S = a/(1r), as follows:
P (Anna wins) = (1/6) / (1  5/12) = 2/7
The answer is 2/7. The probability that Anna wins is the probability that she wins on her first turn or her second turn or her third turn, and so on. The probability distribution, in which we observe a string of failures before the first success is called the geometric probability distribution. The probability that Anna wins on the first roll is 1/6. For Anna to win on the second roll, she must roll any number except 6 on her first roll and Bob must toss tails on his first toss. The probability that Anna wins on the second roll is (5/6)(1/2)(1/6). For Anna to win on the third roll, she and Bob must each have two failures before Anna’s success: (5/6 * ½)^2 * 1/6. So we need to find the sum of infinite geometric series:
P(Anna wins) = 1/6 + (5/6 * ½) * 1/6 + (5/6 * ½)^2 * 1/6 + (5/6 * ½)^3 * 1/6 + 
We use the formula for the sum of an infinite geometric series, S = a/(1r), as follows:
P (Anna wins) = (1/6) / (1  5/12) = 2/7
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
Isn't it 1/12? Probability she rolls a 6 AND Bob lands Tails.indophile wrote:Question # 2. PI got it.
. The probability that Anna wins on the first roll is 1/6
Hellsangel Posts : 14721
Join date : 20110428
Re: Middle School Math Quiz
Hellsangel wrote:Isn't it 1/12? Probability she rolls a 6 AND Bob lands Tails.indophile wrote:Question # 2. PI got it.
. The probability that Anna wins on the first roll is 1/6
If she rolls a 6 she wins. Bob doesnt have to toss.
Mosquito Posts : 706
Join date : 20110428
Re: Middle School Math Quiz
OK. I was interpreting her rolling a 6 AND Bob landing heads to be a draw; and both having to play before you could declare a winner or a draw.PseudoIntellectual wrote:
If she rolls a 6 she wins. Bob doesnt have to toss.
Hellsangel Posts : 14721
Join date : 20110428
Similar topics
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz (no questions on probability)
» Middle School Quiz
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz (no questions on probability)
» Middle School Quiz
Page 1 of 1
Permissions in this forum:
You cannot reply to topics in this forum

